Question

The band has 30 more members than the school chorale. If each group had 10 more members, the ratio of their membership would be 3:2. How many members are in the band? a. 50 members c. 80 members b. 45 members d. 32 members

Answer 1

Answer:

80 members

Step-by-step explanation:

Let the band members be= b and the chorale members=  c

Then, according to question, b=c+30 and $\frac{b+10}{c+10}=\frac{3}{2}$

⇒$2(b+10)=3(c+10)$

⇒$2b+20=3c+30$

⇒$2b-3c=30-20$

⇒$2b-3c=10$

Now, substituting the value of b=c+30, we get

⇒$2(c+30)-3c=10$

⇒$2c+60-3c=10$

⇒$-c=-50$

⇒$c=50$

Therefore, $b=c+30$

$b=50+30=80$

Therefore, there are 80 members in the band.